Equiangular Triangles

  • A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments. A triangle with vertices A, B, and C is denoted triangle ABC.
  • In Euclidean geometry any three non-collinear points determine a unique triangle and a unique plane (i.e. a two-dimensional Euclidean space).

Source: Wikipedia.

 

 

Definition of equiangular triangles:

 

Equiangular Triangle:

           When all the three interior angles are equal for the triangle then it is called as equiangular triangles. All the three interior angles are 60° and also lengths of the sides of triangle are same in length. Equiangular triangles are also called as equilateral triangle.

                                

 

Properties of Equiangular triangles:

 

Equiangular triangle properties are given as

  • In equiangular triangle, all the three sides are in equal length. 
  • Equiangular triangle area formula is given as follow

                         A = `(sqrt(3))/(4)` s2

  • The radius of the incircle is exactly half the radius of the circumcircle.

 

Example problems for equiangular triangles:

Example 1:

Find the area for the given equiangular triangle with length of the side is 6m.

                      

Solution:

           Given

               Length of the side s = 6m

           Equiangular triangle formula

                A = `(sqrt(3))/(4)` S2

                   =   `(sqrt(3))/(4)` 62

                   = `(sqrt(3))/(4)` * 6 * 6

                   = `(sqrt(3))/(4)`* 36

                   =`sqrt(3)`  * 9

                   = 9`sqrt(3)`

                   = 9`sqrt(3)` m2.

Solution to the equiangular triangle area is 9`sqrt(3)` m2 or 15.58 m2.

Example 2:

Find the area for the given equiangular triangle with length of the side is 8m.

                   

Solution:

           Given

               Length of the side s = 8m

           Equiangular triangle formula

                A = `(sqrt(3))/(4)` S2

                   =   `(sqrt(3))/(4)` 82

                   = `(sqrt(3))/(4)` * 8 * 8

                   = `(sqrt(3))/(4)`* 64

                   =`sqrt(3)`  * 16

                   = 16`sqrt(3)`

                   = 16`sqrt(3)` m2.

Solution to the equiangular triangle area is 16`sqrt(3)` m2m or 27.712 m2.

 

Example 3:

Find the length of the sides of given triangle with  one side of length 12 m.

 

<img src="http://image.wistatutor.com/content/feed/u459/111111_0.GIF" mce_src="/files/u459/111111_0.GIF" width="235" height="191">

  

Solution:

Given triangle contains all of its angle is 60°. So the given triangle is called as equiangular triangle or equilateral triangle.

For the length of the sides of equiangular triangle has same length.

For the given equiangular triangle length is 12 m.

So all the length of the sides of the equiangular triangle is 12m.